From a5ca555f2decd8b1a587f65d7f3ecd6fe43ab349 Mon Sep 17 00:00:00 2001
From: hitonanode <32937551+hitonanode@users.noreply.github.com>
Date: Tue, 26 Dec 2023 21:19:38 +0900
Subject: [PATCH] quotients

---
 utilities/quotients.hpp | 26 ++++++++++++++++++++++++++
 utilities/quotients.md  | 17 +++++++++++++++++
 2 files changed, 43 insertions(+)
 create mode 100644 utilities/quotients.hpp
 create mode 100644 utilities/quotients.md

diff --git a/utilities/quotients.hpp b/utilities/quotients.hpp
new file mode 100644
index 00000000..79af1519
--- /dev/null
+++ b/utilities/quotients.hpp
@@ -0,0 +1,26 @@
+#pragma once
+#include <algorithm>
+#include <vector>
+
+// Generate all quotients of n
+// return: n/1, n/2, ..., n
+// Complexity: O(sqrt(n))
+template <class T = long long> std::vector<T> get_quotients(T n) {
+    std::vector<T> res;
+    for (T x = 1;; ++x) {
+        if (x * x >= n) {
+            const int sz = res.size();
+            if (x * x == n) res.push_back(x);
+            res.reserve(res.size() + sz);
+            for (int i = sz - 1; i >= 0; --i) {
+                T tmp = n / res.at(i);
+                if (tmp < x) continue;
+                if (tmp == x and tmp * tmp == n) continue;
+                res.push_back(tmp);
+            }
+            return res;
+        } else {
+            res.push_back(x);
+        }
+    }
+}
diff --git a/utilities/quotients.md b/utilities/quotients.md
new file mode 100644
index 00000000..172be661
--- /dev/null
+++ b/utilities/quotients.md
@@ -0,0 +1,17 @@
+---
+title: 商列挙
+documentation_of: ./quotients.hpp
+---
+
+正の整数 $n$ に対して $\lfloor n / k \rfloor$ （ $k$ は整数）の形で表される整数を昇順に列挙する．計算量は $O(\sqrt{n})$.
+
+## 使用方法
+
+```cpp
+long long n = 10;
+vector<long long> v = get_quotients(n);  // 1, 2, 3, 5, 10
+```
+
+## 問題例
+
+- [Library Checker: Enumerate Quotients](https://judge.yosupo.jp/problem/enumerate_quotients)